how to factor x2 – x – 72

Question

how to factor x2 – x – 72

Answer 1

x^2-x-72

=x^2-9x+8x-72

x(x-9)+8(x-9)

(x-9)(x+8)

 

Answer 2

Another approach:

 

x² -1x - 72,  find 2 factors of 72 whose difference is 1.  (The reason I use the difference is because of -72.  If the last term was positive, I'd use the sum.)

 

The numbers are 9 and 8.

 

try (x - 9)(x + 8);  why not (x + 9)(x - 8)?  Because the first product gives the middle term as -x and the second product gives the middle term as +x.

Answer 3

You need to find two numbers such that when you add the two, you get negative one (coefficient of x), and when you multiply the two, you get -72. So the first step would be factoring 72 and see if we can come up with a pair that would give us the desired result.

 

72 = 2*2*2*3*3*1

 

So now we can choose different pairs based on the factors we have. for example 4 and 18 or 2 and 36. all of these combinations would give us a product of 72, but when we add them up we should get negative one. The fact that the product is -72 means that one of the numbers should be positive, while the other should be negative (since only positive times negative would result in negative), and the fact that the sum should be negative one means that the larger number should be negative. 

 

Looking carefully at the factors of 72, we see that -9 and 8 works well, as -9*8=72 and -9+8=-1

 

Note: you get the 9 from 3*3,  and the 8 from 2*2*2 

 

so (x-9)(x+8)     would be your answer.